A073890 -id:A073890 - cp's OEIS frontend

A075119 Denominator of n/floor(sqrt(n)); numerator is A073890(n).

1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 3, 1, 3, 3, 1, 1, 4, 2, 4, 1, 4, 2, 4, 1, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 1, 6, 3, 2, 3, 6, 1, 6, 3, 2, 3, 6, 1, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 1, 8, 4, 8, 2, 8, 4, 8, 1, 8, 4, 8, 2, 8, 4, 8, 1, 1, 9, 9, 3, 9, 9, 3, 9, 9, 1, 9, 9, 3, 9, 9, 3, 9, 9, 1, 1, 10, 5, 10, 5

Offset: 1

Reinhard Zumkeller, Sep 03 2002

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000196, A067815.

import Data.Ratio ((%), denominator)
a075119 n = denominator $ n % a000196 n
-- Reinhard Zumkeller, Jul 08 2014

A075119:=n->denom(n/floor(sqrt(n))): seq(A075119(n), n=1..100); # Wesley Ivan Hurt, Jul 07 2014

Table[Denominator[n/Floor[Sqrt[n]]], {n, 100}] (* Wesley Ivan Hurt, Jul 07 2014 *)

a(n) = A000196(n)/A067815(n).

Numerator reference corrected by Reinhard Zumkeller, Jul 08 2014

A067815 a(n) = gcd(n, floor(sqrt(n))).

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 3, 1, 1, 3, 4, 1, 2, 1, 4, 1, 2, 1, 4, 5, 1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 6, 1, 2, 3, 2, 1, 6, 1, 2, 3, 2, 1, 6, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 8, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 8, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9

Offset: 1

Reinhard Zumkeller, Feb 08 2002

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000196, A073890, A075119.

a067815 n = gcd n $ a000196 n  -- Reinhard Zumkeller, Jul 08 2014

a[n_] := GCD[n, Floor[Sqrt[n]]]; Array[a, 100] (* Amiram Eldar, Nov 19 2024 *)

a(n) = gcd(n, sqrtint(n)); \\ Altug Alkan, Dec 19 2017

A075120 Number of steps to reach the first integer (= A075121(n)) starting with n/floor(sqrt(n)) and iterating the map x -> x*ceiling(x), or -1 if no integer is ever reached.

Original entry on oeis.org

0, 0, 0, 0, 2, 0, 1, 0, 0, 5, 2, 0, 3, 2, 0, 0, 3, 3, 2, 0, 2, 1, 3, 0, 0, 8, 3, 5, 2, 0, 3, 2, 5, 3, 0, 0, 6, 2, 2, 4, 2, 0, 5, 3, 1, 4, 2, 0, 0, 7, 12, 5, 11, 12, 2, 0, 4, 3, 9, 12, 6, 16, 0, 0, 3, 7, 8, 4, 4, 4, 2, 0, 2, 4, 5, 1, 5, 2, 5, 0, 0, 7, 3, 22, 3, 3

Offset: 1

Reinhard Zumkeller, Sep 03 2002

nonn

Starting with A073890(n)/A075119(n).

			a(13)=3 since 13/floor(sqrt(13)) = 13/3 -> 65/3 -> 1430/3 -> 227370 = A075121(13).

Cf. A068119, A073524, A075102, A075107, A075121.

More terms from Jinyuan Wang, Jan 15 2022

cp's OEIS Frontend

A075119 Denominator of n/floor(sqrt(n)); numerator is A073890(n).

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A067815 a(n) = gcd(n, floor(sqrt(n))).

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A075120 Number of steps to reach the first integer (= A075121(n)) starting with n/floor(sqrt(n)) and iterating the map x -> x*ceiling(x), or -1 if no integer is ever reached.

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